Acharyya, Sudip KumarChattopadhyaya, K.C.Ghosh, Partha Pratim2017-06-082017-06-082004-04-011576-9402https://riunet.upv.es/handle/10251/82550[EN] The main aim of this paper is to investigate a subring of the ring of continuous functions on a topological space X with values in a linearly ordered field F equipped with its order topology, namely the ring of continuous functions with compact support. Unless X is compact, these rings are commutative rings without unity. However, unlike many other commutative rings without unity, these rings turn out to have some nice properties, essentially in determining the property of X being locally compact non-compact or the property of X being nowhere locally compact. Also, one can associate with these rings a topological space resembling the structure space of a commutative ring with unity, such that the classical Banach Stone Theorem can be generalized to the case when the range field is that of the reals.Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Ordered FieldsZero Dimensional SpacesStrongly Zero Dimensional SpacesCompactificationsArtículo2017-06-0810.4995/agt.2004.1999Abierto1989-4147